Parallelisms of Complete Designs

These notes present an investigation of a condition similar to Euclid's parallel axiom for subsets of finite sets.

Peter J. Cameron (Author)

9780521211604, Cambridge University Press

Paperback, published 10 June 1976

152 pages
22.9 x 15.2 x 1 cm, 0.234 kg

These notes present an investigation of a condition similar to Euclid's parallel axiom for subsets of finite sets. The background material to the theory of parallelisms is introduced and the author then describes the links this theory has with other topics from the whole range of combinatorial theory and permutation groups. These include network flows, perfect codes, Latin squares, block designs and multiply-transitive permutation groups, and long and detailed appendices are provided to serve as introductions to these various subjects. Many of the results are published for the first time.

Introduction
1. The existence theorem
Appendix: the integrity theorem for network flows
2. The parallelogram property
Appendix: the binary perfect code theorem
Appendix: association schemes and metrically regular graphs
3. Steiner points and Veblen points
Appendix: Steiner systems
4. Minimal edge-colourings of complete graphs
Appendix: latin squares, SDRs and permanents
5. Biplanes and metric regularity
Appendix: symmetric designs
6. Automorphism groups
Appendix: multiply transitive groups
7. Resolutions and partition systems
Bibliography
Index.

Subject Areas: Mathematical foundations [PBC]